Vehicle range analysis using driving environment information with optional continuous averaging

ABSTRACT

Determining remaining vehicle range by adjusting measured estimates on the fly accounting for road effects, the state of vehicle accessories, and other conditions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/713,075 which was filed on Oct. 12, 2012, byPablo A. Vicharelli et al. for “VEHICLE RANGE ANALYSIS USING ENVIRONMENTINFORMATION AND/OR CONTINUOUS AVERAGING”; and is a Continuation-in-partof U.S. patent application Ser. No. 13/650,325, which was filed on Oct.12, 2012, by Pablo A. Vicharelli et al. for a METHOD AND SYSTEM FORVEHICLE RANGE ANALYSIS; both of which are hereby incorporated byreference.

BACKGROUND

1. Technical Field

This application relates to a method for estimating a vehicle's range ordistance it will travel before it runs out of fuel and more specificallyto using a combination of measured data and calculations to extend theapplicability of such analysis to range predictions for a plurality ofdriving environments not considered in the measurements.

2. Background

The range of a vehicle is usually specified by the manufacturer assuminga set of conditions such as flat terrain, driving environment (city,highway) and a specified weight. The actual range obtained by a driverwill depend on speed, terrain, cargo, climate control, driving style andother factors. This range variation applies to both electric andinternal combustion vehicles. However, drivers of gasoline vehicles havean extensive network of gas stations available to them while drivers ofelectric vehicles fear that they might be stranded if they run out ofcharge with no charging station nearby. This uncertainty in the rangeleads to what is called “range anxiety.” To alleviate this anxiety,automakers provide built-in navigation systems that provide maps withthe locations and directions to the closest charging stations, as wellas a circle map overlay that indicates graphically the range of the car,i.e., the range is turned into the radius of a circle. All electricvehicles provide some sort of graphical bar display that indicates theamount of charge remaining in the battery and/or the range, a singlenumber.

There are two main approaches for the determination of the range of avehicle: (a) measurements, and (b) detailed mathematical modeling. Therange of a vehicle is typically measured in a laboratory with the helpof a dynamometer that simulates the driving environment. The measurementincludes rolling resistance under flat terrain conditions for severalsimulated driving schedules designed to simulate, e.g., city and highwaydriving. Three additional tests are available to account for higherspeeds, air conditioning use, and colder temperatures. FIG. 1 providesdetails for all five United States' Environment Protection Agency (EPA)test schedules, which apply to vehicles with internal combustionengines. The EPA is currently working to establish somewhat differenttesting criteria for electric vehicles and plug-in hybrids.

This kind of measurement usually includes the effect of vehicle weightand aerodynamic drag by adjusting the energy required to move thedynamometer rollers. Range is reported as a distance, e.g., 100 mi, foreach driving environment, ambient temperature, and which accessories areturned on for a tank full of fuel or a fully charged battery.

Some current navigation systems display the measured range as a circularcontour, implying that locations inside the contour can be reached bythe vehicle. The idea there is that as the fuel level or battery chargedecreases, the circle radius will decrease accordingly. A sample displayis shown in FIG. 2. Even though this display is supposed to take intoaccount the remaining battery charge, current location, and drivingconditions, it is overly optimistic. The reason is that this rangeestimate reflects EPA-type or vehicle manufacturer's measurements, whichlikely do not include terrain variations, the effects of driving onactual roads, changes in the driving surface, or the actual drivingspeeds.

SUMMARY

Of these effects, perhaps the most important is the constraint thatvehicles are usually required to follow roads and obey trafficregulations, e.g., one-way signs, as opposed to the straight lineassumed by the prior art. Therefore, a need exists for more accuratelycomputing a vehicle's range for more realistic driving environments.Furthermore, a more accurate map display of the range for a single tripor for the construction of a maximum range contour, i.e., trips in allpossible directions, is also needed. Our initial motivation is theapplication to electric vehicles, but naturally, the analysis applies aswell to vehicles based on internal combustion engines, hydrogen fuelcells, etc. So we will use the terms fuel, electric charge, or justcharge, interchangeably.

It is an advantage of our approach that range analysis starts out with ameasured range and subsequently adjusts it to account for factors notincluded in the original measurements. Thus, this approach is based onmodeling done relative to the conditions used in quantifying measuredvehicle range by calculating contributions that either penalize orenhance the measured range. For concreteness, we discuss EPAmeasurements here, but the range could come from any measurement, evenfrom real time measurements from within the vehicle itself. In addition,the reference data could be produced by some other detailed mathematicalmodel for range and the methods described here could be used to extendits applicability.

The model is made more realistic by simulating driving by followingactual roads, instead of the straight-line “as the crow flies” drivingpath implied by the EPA measurements and implemented in the sample rangedisplay of FIG. 2. In addition, we optionally include the effects due tochanging driving surface conditions, which in turn affect the rollingresistance. Aerodynamic drag effects are also incorporated in themodeling when average speeds are available for various road types.Finally, terrain effects are also taken into account; goinguphill/downhill can decrease/increase the range.

The modeling is preferably done within the framework of a computerizedsystem that provides the necessary road information database and routingcapabilities for driving from one location to another. It could thusnaturally be implemented in existing vehicle navigation systems hardwareand software, in one embodiment.

In a preferred arrangement, the range estimates that depend on roadconditions are then further adjusted by taking into account the state ofaccessories that may further affect range, such as air conditioningsystems and the like.

These estimates of the affects on the maximum range due to the roadconditions and is accessory state can then further be averaged on thefly continuously. The result is improved estimate of the expectedmaximum range.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages, which are notmeant to be limiting, will be apparent from the following moreparticular description of preferred embodiments, as illustrated in theaccompanying drawings in which like reference characters refer to thesame parts throughout the different views.

FIG. 1 illustrates the common driving schedules currently used tomeasure fuel efficiency and range;

FIG. 2 is an illustration showing a prior art display of vehicle range;

FIG. 3 is a schematic representation some possible routes to get fromlocation A to location B in an idealized city where all the blocks arethe same size;

FIG. 4 is a schematic representation of a single-route range analysisusing roads;

FIG. 5 is a schematic representation of an arbitrary driving route frompoint A to point B;

FIG. 6 is a flowchart of the process for analyzing a single drive routeusing road information;

FIG. 7 is map display with sample range analysis results for a singleroute using road information;

FIG. 8 is a flowchart of the process for calculating points for acolor-coded range contour;

FIG. 9 is a schematic representation of the variables involved incalculating a range contour;

FIG. 10 is a flowchart of the process for calculating a single point ofa range contour.

FIG. 11 is a map display with a sample range contour;

FIGS. 12( a) and 12(b) are a schematic display of the variables involvedin calculating tractive effect contributions to the vehicle rangecalculation;

FIG. 13 is a flowchart of the process for the continuous averaging ofthe maximum range for multiple driving environments;

FIG. 14 is a schematic representation of a driving schedule for drivingthrough city and highway environments;

FIG. 15 is a graph of the continuously-averaged maximum range for a tripthrough city and highway environments;

FIG. 16 is a graph of the continuously-averaged maximum range for a tripthrough city and highway environments with the air conditioning turnedoff and on;

FIG. 17 is an illustration of a representative apparatus;

FIG. 18 is a flowchart of the process for analyzing vehicle range in arepresentative apparatus; and

FIG. 19 is a flowchart of the process for calculating range for bothsingle route and contours.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

The following detailed description is merely exemplary in nature and isnot intended to limit the invention as claimed or its application anduses. For most driving environments perhaps the largest impact onvehicle range comes from the fact that vehicles must (usually) followthe roads. Our approach therefore begins with road effects.

Consider a vehicle whose range D_(max) that has been determined frommeasurements in a flat terrain environment, and only one type of roadsurface such as described in the EPA schedules of FIG. 1. In terms ofdriving range, this value is usually all that is reported by the vehiclemanufacturer. One aspect here generalizes this approach and provides amore realistic estimate of range. Starting from the current vehiclelocation we obtain a contour that defines how far we can drive before werun out of fuel or charge (more generally, “energy”). This would give usa graphical (or geographical) sense of the range in two dimensions,i.e., on a map. If we are driving along flat terrain radially outward,the contour would be a circle with radius D_(max). Typical contoursmight look like those in FIG. 2. Such a simple contour 222 or 224, whichis what is currently provided by some manufacturers of electricvehicles, assumes that we drive only along the radial direction, i.e.,constant azimuth angle away from the starting location. But thisscenario would only present the exact result for cases where one candrive radially outward without any regard for roads, i.e., to caseswhere there are no roads and the vehicle can traverse them, as in adesert. It is a very simplistic approach to getting from point A topoint B by choosing the shortest path. This path is a great circle arc,which approaches a straight line for short distances.

In practice, vehicles usually must follow existing roads, and the momentwe deviate from the straight line A-B path we end up driving longer.This extra driving could, in general, lead to appreciably longer drivingdistances, which might mean that we could run out of fuel or chargebefore we get to our destination. This is illustrated in FIG. 3 where weshow a schematic of some ideal city 342 where the blocks are all thesame size. Here we see that the optimal, i.e., straight-line, route 345that goes from A to B has a length of 5 in block units. However, if theexisting roads, including one-way restrictions, etc., force us to go dueeast, then north, and finally west, we would have driven 8 blocks, asindicated by 346 (Route 1). This means that the more realistic route is60% longer, implying that it would use 60% more fuel/charge. Thisrepresents a huge fuel efficiency penalty just by following the roads.Naturally, if we could stay as close as possible to the A-B path wewould expect a smaller penalty. To do that we would have to zig-zagabout the straight line route. An example of a zig-zag route 347 is alsogiven in FIG. 3, where we see that this route (Route 2) would travel for7 blocks. The penalty in this case is 40%, which is smaller than in theprevious example, but still quite significant. In fact, even in the verysimple case where we wish to travel from a corner in a block to thediagonally opposite corner, the straight-line distance is sqrt(2)=1.41blocks, while the realistic going around the block distance is 2 blocks.In this case the penalty is about 42%.

So, the penalty could range from negligible, for paths that mostlyfollow a single road, i.e., horizontally or vertically in FIG. 3, togreater than 40%, for short (˜10-20 mi), roughly diagonal paths. Animportant point to make here is that since the vehicle-driving-distancepenalties vary over such wide range depending on orientation, thecircular contour currently used is not very meaningful. In fact, ifvehicles follow roads most of the time, all these possibilities will beencountered when defining a contour, i.e., as we imagine drawing radialsover 360 degrees. As we might expect, the contour would exhibitsignificant deviations from a circular shape.

Our approach in one embodiment quantifies the effects of needing tofollow the roads. We start with a single A to B path such as the oneillustrated in FIG. 4. The endpoints could be defined by the coordinates(latitude and longitude) of the A and B points, or by their streetaddresses. Point 447 is arbitrary and the end point 448 represents alocation at a distance equal to the maximum range of a vehicle, givensome amount of fuel in the tank/battery. The distance along a straightline path 453 connecting points A and B, D_(max), would represent thebest that we can do in terms of shortest distance and it will be ourreference value. Then, we try to come up with a driving route that mostclosely approximates it, given the details of the local roads andone-way restrictions. This route could be obtained by algorithms such asthose used by vehicle navigation systems or by Google maps. Such a route449, 452, and 450, could be obtained based on various criteria (shortestdistance, most use of highways, etc.); we will base it on the shortestdistance for now. The route will be provided as an array of waypoints516 such as those schematically illustrated in FIG. 5. The k-th elementof this array is represented by p_(k). The total distance will then becalculated by adding the individual waypoint to waypoint distances,

$\begin{matrix}{D_{T} = {\sum\limits_{k = 1}^{N - 1}\; d_{k}}} & (1)\end{matrix}$

where D_(T) is the total route distance, d_(k) is the distance 518between the waypoints with is indices k+1 and k,

d _(k) =p _(k+1) −p _(k),   (2)

and N is the number of waypoints in the route, which means we have N−1road distances or segments. In general, for a given pair of A and Blocations the distance D_(T) will be larger than the distance D_(max) ifwe follow the roads. We will be interested in a partial summation givenby

$\begin{matrix}{{D_{\max} = {\sum\limits_{k = 1}^{n}\; d_{k}}},{n \leq {\left( {N - 1} \right).}}} & (3)\end{matrix}$

In other words, as we follow the roads when going from A to B, we willreach the distance D_(max), the point where we would run out offuel/charge, and therefore not be able to reach B. So, a particulardrive route is analyzed by adding the terms in the summation above,until we reach D_(max). The corresponding index n will indicate whichwaypoint we were able to reach. In practice, it is unlikely that thewaypoint will hit the D_(max) value exactly. Most of the time we willovershoot when using the above summation, and in this case we will needto interpolate to find the actual location.

The straight-line A to B path is shown as a dashed line 453 in FIG. 4.The circle 446 represents the “no-roads” contour, centered at A with aradius D_(max). Even though point B 448 is inside the circular contour,the existing roads force the driver to follow a route that ends upexhausting the fuel/charge before reaching the destination point B. Theexample route has been obtained from Google maps using actual streets ina suburb of Boston. The route is displayed as three segments—black 449,grey 452, and white 450. The color coding is as follows: We start outwith a full tank of fuel (or a fully charged battery) and we analyze theroute distance to find the point where we run out of fuel. Then thesegment 449 from A to this point is displayed as black. The rest of theroute, which in principle is not accessible because we have no morefuel, is displayed as a white segment. Since fuel/charge gauges are notexact but will have some error, assume, for example, +/−δ%, the black towhite transition will not occur at a single point, but rather, it willbe spread over some distance, +/−δ% of the length of the black segmentfor this example. This uncertainty is illustrated by the grey segment452 in the route of FIG. 4. The route differs so much from the dashedline that it runs out of fuel somewhere in the grey segment. Again, thisuses actual roads. The white segment 450 represents unreachablelocations.

Naturally, the color scheme is totally arbitrary. In our preferredembodiment we select green for segments that are reachable, red forsegments that are unreachable, and yellow for uncertain locationsbetween the green and red segments. The steps involved in thecalculation of this type of color-coded analysis of the vehicle rangeare summarized in the flowchart of FIG. 6 and a sample route calculatedwith actual map data for the area 740 around Boulder, Colo., is shown inFIG. 7. The simulation starts at a downtown location 742, and ends at alocation in the nearby foothills 744. We assume there is just enoughfuel to reach the destination location, indicated by the circularcontour 752 and that the fuel/charge indicator has a 10% accuracy. Acalculation 627 of the shortest route results in a route constructedfrom segments 746, 748, and 750. The present method predicts that thevehicle would only reach locations within the black segment 746 andperhaps to some locations within the grey segment 748, while the priorstate of the art erroneously predicts that it would reach itsdestination 744 because this location is just inside the circle.

A more realistic contour that takes into account the roads involved inthe route can be calculated by selecting multiple radials. Preferablythe radials would be evenly spaced around 360 degrees, but that is not arequirement and any angular separation could be used. The flowchart inFIG. 8 illustrates the steps of this process. The radials areconstructed so that the A to B straight-line distance equals the givenD_(max) that corresponds to the specified range of the vehicle underconsideration. In effect, the measured range defines a circularreference contour. Now we select an azimuth angle for the A to B radial.If A and B happened to be connected by a road, then point B wouldrepresent the contour point for this radial. However, when we invoke therouting module 804 to arrive at a route that follows the roads, it ismore likely that we could, for example arrive at some point C in FIG. 9.This point 935 represents the closest we are able come to thedestination B before we run out of fuel. Notice that the radial thatgoes from A to C could in general have a different angle 937 and radialdistance 942 when compared with the original angle 938 and distance 941.So the AB radial 941 is replaced by the AC radial 942, and we proceed tothe next radial. This process is repeated until the desired number ofradials is calculated as illustrated in FIG. 10. An example of a typicalcontour obtained this way including the tractive effects discussed belowis shown in FIG. 11. The deviation from the reference circle can bequite large, coverage is about 40% of the area of the circle.

In order to make the modeling more realistic we can also includetractive effects and we also use the measured range D_(max) to estimatethe available energy for the conditions corresponding to the EPA tests.Then, we equate this energy to the energy calculated by our model—thisleaves our calculated range as an unknown parameter. Next, we use ourmodel to simulate driving along the route until we run out of energy andwe record the location where this happens. This is as far as the vehiclewill be able to go without additional charging. Finally, we report thislocation to the driver, either by specifying the lat-long, thecorresponding address, or by color-coding the drive route on thenavigation system display.

Modeling Tractive Effects

Consider the movement of a vehicle from point A to point B along path Sas schematically illustrated in FIG. 5. The work done is given by

W _(A→B)=∫_(A) ^(B) F _(T) ·ds   (4)

where F_(T) is the total tractive force or road load given by

F _(T) =F _(R) +F _(H) +F _(A) +G.   (5)

Here F_(R) is the rolling resistance force, F_(H) is the hill climbingforce, F_(A) is the aerodynamic drag, and G is a term that representsall other forces, e.g., braking, and driver-dependent effects such asacceleration/deceleration during stop-and-go driving. The U.S.Department of Energy (DOE) has published some estimates of brakinglosses for city, highway, and combined city/highway driving. We can usethose estimates for the G term as representatives values for an averagedriving style.

Since our modeling is based on paths described by arrays oflatitude-longitude points, we can use these points to constructstraight-line segments that can be used to approximate the integral ofEq. (4). In addition, since the motion will be parallel to the segmentswe can write

$\begin{matrix}{{W_{A\rightarrow B} \cong {\sum\limits_{k = 1}^{N - 1}\; {{F_{T}(k)}s_{k}}}},} & (6)\end{matrix}$

where F_(T)(k) is the force along the road segment, N is the number ofwaypoints, N−1 is the number of segments for the A to B route, and s_(k)is the length of the k-th segment. With the help of the coordinatesshown in FIG. 12, the forces associated with a segment can be written as

$\begin{matrix}{{F_{R}(k)} = {\mu_{k}{mg}\; {\cos \left( \theta_{k} \right)}}} & (7) \\{{{F_{H}(k)} = {{mg}\; \sin \; \left( \theta_{k} \right)}}{and}} & (8) \\{{F_{A}(k)} = {\frac{1}{2}\rho \; v_{k}^{2}C_{D}A}} & (9)\end{matrix}$

Here μ_(k) is the coefficient of rolling resistance, m is the mass ofthe vehicle, g is the acceleration of gravity, θ_(k) is the road slopeangle, ρ is the air density, v_(k) is the air velocity relative to thevehicle, C_(D) is the drag coefficient, and A is the frontal area of thevehicle.

Since the measurements and the actual driving could also include caseswhere the accessories, e.g. the air conditioning or heater, are turnedon or off, we would need to add an extra term W_(acc) to account forthis. This term is not a tractive term, but it is an energy loss, so itis convenient to incorporate it as part of the work done. Forconsistency, we break up this energy into a sum of contributions overall route segments. In other words, we assume that we can define aneffective accessory energy density H(k) so that we write

$\begin{matrix}{W_{acc} = {{\sum\limits_{k = 1}^{N}\; {W_{acc}(k)}} = {\sum\limits_{k = 1}^{N}\; {{H(k)}{s_{k}.}}}}} & (10)\end{matrix}$

The energy density H(k) is represented as an array of values thatcorrespond to the array of road segments. It could have some backgroundvalue for road segments s_(k) where the accessory is off and then go tosome characteristic value of the accessory energy consumption for thesegments where it is on. One could also have multiple steps if, forexample, the heater/AC has multiple temperature settings.

Putting it all together we find that the work done in going from point Ato B would be

$\begin{matrix}\begin{matrix}{W_{model} = {\sum\limits_{k}^{N}\; {\left\lbrack {{F_{R}(k)} + {F_{H}(k)} + {F_{A}(k)} + {G(k)} + {H(k)}} \right\rbrack s_{k}}}} \\{= {\sum\limits_{k}^{N}{\left\lbrack {{\mu_{k}{mg}\; {\cos \left( \theta_{k} \right)}} + {{mg}\; {\sin \left( \theta_{k} \right)}} + {\frac{1}{2}\rho \; v_{k}^{2}C_{D}A} + {G(k)} + {H(k)}} \right\rbrack s_{k}}}}\end{matrix} & (11)\end{matrix}$

Now let's connect this model to the EPA measurements, whose main resultis a reported maximum range D_(max). All the other quantities aredetermined from the test schedule. A single rolling resistancecoefficient, which we can call μ_(ave) is used, the angle θ_(k) goes tozero for flat terrain, v_(k) is replaced by the corresponding averagespeed for city or highway driving, and G and H are also replaced bytheir averages. We get

$\begin{matrix}{W_{meas} = {\left\lbrack {{\mu_{ave}{mg}} + {\frac{1}{2}\rho \; v_{ave}^{2}C_{D}A} + G_{ave} + H_{ave}} \right\rbrack {D_{\max}.}}} & (12)\end{matrix}$

The equation for W_(meas) gives us the energy spent to reach distanceD_(max), so it is reasonable to assume that the same energy is availablefor our modeling. Setting the last two equations equal to each other weget,

$\begin{matrix}{\mspace{79mu} {{W_{model} = W_{meas}},\mspace{79mu} {or},}} & (13) \\{{\sum\limits_{k}^{n \leq N}\; {\left\lbrack {{\mu_{k}{mg}\; {\cos \left( \theta_{k} \right)}} + {{mg}\; {\sin \left( \theta_{k} \right)}} + {\frac{1}{2}\rho \; v_{k}^{2}C_{D}A} + {G(k)} + {H(k)}} \right\rbrack s_{k}}} = {\left\lbrack {{\mu_{ave}{mg}} + {\frac{1}{2}\rho \; v_{ave}^{2}C_{D}A} + G_{ave} + H_{ave}} \right\rbrack D_{\max}}} & (14)\end{matrix}$

This relationship can be re-written in the more compact form

$\begin{matrix}{{{\sum\limits_{k}^{n \leq N}{\alpha_{k}d_{k}}} = D_{\max}}{where}} & (15) \\{d_{k} = {s_{k}{\cos \left( \theta_{k} \right)}}} & (16)\end{matrix}$

is the projection 1222 of the k-th segment length 1221 on the ground, asshown in FIG. 12 and

$\begin{matrix}{\alpha_{k} = {\frac{1}{\left( {1 + \Gamma} \right)\left( {1 + \Delta} \right)}\left\lbrack {\left( \frac{\mu_{k}}{\mu_{ave}} \right) + \left( \frac{\tan \left( \theta_{k} \right)}{\mu_{ave}} \right) + {\Gamma \; {\sec \left( \theta_{k} \right)}\left( \frac{v_{k}}{v_{ave}} \right)^{2}} + {{\Delta \left( {1 + \Gamma} \right)}\sec \; \left( \theta_{k} \right)\left( \frac{G_{k} + H_{k\;}}{G_{ave} + H_{ave}} \right)}} \right\rbrack}} & (17)\end{matrix}$

acts as a coefficient that weighs the contributions for each roadsegment. This is our main result. Eq. (15) models the calculated rangeas a sum of weighted route segments. It is similar to Eq. (3), which wasderived for the case that only includes the restriction that we mustdrive on the roads. Just as we did before, we can simulate driving alongeach segment and adding up the individual contributions until thesummation matches the measured D_(max). The upper summation limit in Eq.(15) has been modified to account for the fact that the vehicle beingmodeled might run out of fuel/charge before it reaches the last routesegment. If the weight α_(k) is greater than one it acts as a penaltybecause we reach D_(max) sooner and we might not reach point B.Conversely, if it is less than one or even negative, it enhances thecalculated range. So our problem reduces to estimating the values of theα_(k) weights.

Eq. (15) could be expressed in terms of s_(k), but we prefer d_(k) sinceit is a projected distance that is usually reported by navigationsystems. In other words, navigation systems usually do not account forterrain variations, and if we're working with one that does, we simplytake that into account.

Vehicle Fuel Efficiency in Mixed Driving Environments

The EPA typically reports vehicle fuel efficiency data as miles pergallon (mpg) ratings for two types of driving environments, city andhighway. It also reports a combined rating, which is a weighted averageof the two. Letting E represent the mpg we can write

E _(comb) =a _(city) E _(city) +a _(hwy) E _(hwy)   (18)

where the EPA weight a_(city) and a_(hwy) are set to 0.55 and 0.45,respectively.

This can be modified to account for the actual environment being drivenor planned to be driven for a trip. Consider a drive route with N+1waypoints. We construct an array of N road segments defined by onewaypoint to the next. As we imagine driving along this route segment bysegment, we record whether we're driving in the city or on a highway.Then we count the number of segments that lie in the city. This number,normalized to the total number of segments, yields the actual weight forcity driving,

$\begin{matrix}{{{a_{city}(N)} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}\; g_{j}^{city}}}}{where}} & (19) \\{g_{j}^{city} = \left\{ \begin{matrix}{1,} & {{if}\mspace{14mu} j\text{-}{th}\mspace{14mu} {segment}\mspace{14mu} {is}\mspace{14mu} {in}\mspace{14mu} {the}\mspace{14mu} {city}} \\{0,} & {otherwise}\end{matrix} \right.} & (20)\end{matrix}$

The highway weight can evaluated using a similar summation, but sincethe weights should be normalized, it is more convenient to calculate itfrom

a _(hwy)=1−a _(city)   (21)

This approach would give a much better estimate of the combinedefficiency rating, at the expense of analyzing the route segment bysegment. This type of treatment can be along an actual route generalizedto the case of M environments and partial trips. Again, starting with anarray of N road segments, when we simulate driving up to the k-thsegment, we write

$\begin{matrix}{{{a_{m}(k)} = {\frac{1}{k}{\sum\limits_{j = 1}^{k}\; \delta_{{e{(j)}},m}}}}{with}} & (22) \\{\delta_{{e{(j)}},m} = \left\{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {e(j)}} = m} \\{0,} & {otherwise}\end{matrix} \right.} & (23)\end{matrix}$

Here e(j) is the environment ID for the j-th segment, with e(j)={1, 2, .. . , M}, δ is a Kronecker delta, and a_(m)(k) is the (city or highway)cumulative weight for the m-th environment for a trip that has gone tothe k-th segment. Then, the combined fuel efficiency up to the k-thsegment will be given by

$\begin{matrix}{{{E_{comb}(k)} = {\sum\limits_{m = 1}^{M}\; {{a_{m}(k)}E_{m}}}},{k \leq N}} & (24)\end{matrix}$

This is a quantity that can be computed/updated while the vehicle ismoving if we have access to its location coordinates, perhaps from a GPSdevice, and to information about the environment at that location. Thelatter can be obtained from digital road maps, which contain a wealth ofinformation about whether a particular road is a highway, a secondaryroad, etc. The fact that the EPA reports only two environmentssimplifies the calculation significantly. However, if at a later time wecould have more environments measured and their fuel efficienciesreported, the road maps and the equations above would allow moreaccurate combined estimates. For areas where roads are available, buttype information is sparse or nonexistent, one can add other sources,such as Land Use and Land Cover (LULC) maps provided by the U.S.Geological Survey and other international agencies to the road typeanalysis. These maps are quantized into raster pixel areas (e.g., 30×30m pixels) that contain raster information that tells us if an area is anurban, suburban, rural, etc., environment. LULC maps are frequently usedin computer programs that predict wireless signal propagation.

This method of calculating the weights can also be applied to theaveraging of the vehicle range used the Range Analysis described above.We write

$\begin{matrix}{{{D_{comb}(k)} = {\sum\limits_{m = 1}^{M}\; {{a_{m}(k)}D_{m}}}},{k \leq N}} & (24)\end{matrix}$

where a_(m)(k) is as defined above, D_(m) is the maximum rangeassociated with environment m, with m={city, highway, . . . }, andD_(comb)(k) is the combined maximum range evaluated up to segment k. Inother words, it is a combined range that is updated dynamically as thevehicle travels.

To incorporate the dynamic variations to the combined range into ouranalysis we then replace D_(max) with D_(comb)(n) in Eq. (15) above.This substitution results in the following equation

$\begin{matrix}{{\sum\limits_{k}^{n \leq N}\; {\alpha_{k}d_{k}}} = {{D_{comb}(n)}.}} & (24)\end{matrix}$

where n is the maximum value of k in a progression of partial summationsas n ranges from 1 to N. As outlined above, this equation is used tosimulate driving along each segment d_(k), adding up the individualsegment contributions while monitoring the value of the summation foreach value of n. We stop the simulation when the summation on theleft-hand side matches the combined maximum range of the right-handside.

Averaging Range Estimates on the Fly

While improved combined fuel efficiency ratings estimated according tothe above equations could be useful in some applications, the averagingdone for the max ranges can become important in improving the accuracyof the range analysis as the vehicle moves. This model, as explainedabove, simply uses a max range D_(max) that could be city, highway, orcombined (meaning 55/45). With this additional modeling, it could use amuch better estimate of the combined range generated on the fly.

The steps involved in calculating this averaging on the fly are outlinedin FIG. 13 for the case of two environments, city and highway. In afirst step 1672, route waypoints are determined. These waypoints arethen used to construct the road segments 1673 and from the segmentsdetermine the driving environment 1674. Subsequently, the normalizedweights are calculated from the sum of steps 1676 to 1678. Finally, instep 1680 the range is calculated as the weighted average of the cityand highway ranges.

An additional benefit of this type of continuous averaging is that itallows the analysis of a vehicle's range also taking into considerationthe on/off state of accessories such as the AC or heater. For example,the following table summarizes some typical straight-line ranges for atypical electric passenger car, the Nissan Leaf:

Environment Max Range, AC On Max Range, AC Off City 47 mi 105 mi Highway70 mi 138 mi Combined (55/45) 57 mi 120 mi

The numerical values shown in this table represent the D_(m) terms inthe equation above. As we can see, whether the AC is on or off has alarge impact on the maximum range of this vehicle.

To illustrate how this affects a range analysis calculation we cansimulate a 20 mi trip with the simple city/highway schedule of FIG. 14.This schedule consists of alternating city/highway sections that havebeen designed to match the EPA's overall 55/45 weights. It follows thatfor the case of AC off, the combined maximum range is 120 mi.

Application of the present averaging technique results in the maximumrange variations illustrated in FIG. 15. Here one can clearly see thatthe range is below the 120 mi value throughout most of the trip, and itdoes not approach the combined EPA-like maximum until the end. This canhave a significant impact in the range analysis calculation, whoseresults will be more realistic if we use the continuously averagedmaximum range of FIG. 15 instead of the single average range.

The continuous averaging described here can be applied simultaneously toboth the changes in environment and to the on/off state of the AC.Assume that the AC is initially off as we start traversing the drivingschedule of FIG. 14. This selects a set of D_(m) maximum ranges from thetable above and the combined average range would resemble that of FIG.15 as we simulate driving through the schedule. Then, we arbitrarilyassume it is turned on after 8 mi into the trip. At this point the userinput component 1345 would alert the range analyzer 1346 that the AC isnow on, which would result in the selection of a different set of D_(m)ranges from the table. The averaging continues with the new set ofparameters until the simulation reaches the end of the trip. Theresulting maximum range values are summarized in FIG. 16. Turning on theAC has a very dramatic impact on maximum range, and subsequently, on therange-analysis results. In this particular case, the driver will be ableto immediately see the impact that the AC will have on the range contouror color-coded route and perhaps turn it off if the destination or afueling/charging station might not be reached.

This averaging will improve the results of the methods in the patentapplication cited above that was filed on Oct. 12, 2012, by Pablo A.Vicharelli et al. for a METHOD AND SYSTEM FOR VEHICLE RANGE ANALYSIS”which focuses on tractive effects. In addition, it lets us handle theaccessories being on/off in a simpler, more accurate way. If we havedata like that in the table above, we could now ignore the “H force”term and use accessory on/off ranges D_(m) directly.

Displaying Range Information

Our approach includes unique ways of displaying range information. FIG.11 shows some predicted results overlaid on a map 1160 for a vehicle1176 located in downtown Boulder, Colo. This region was chosen becauseit contains very rugged terrain to the west of the city, while to theeast the terrain is relatively flat with some gentle slopes down in somedirections. The black circle 1162 corresponds to the coverage predictedby the current state of the art for a given amount of fuel/charge. Theshaded area 1164 corresponds to the locations that can be reached by thevehicle according to the present model after correcting the referenceresults for road effects and terrain. The reduction in coverage is quitedramatic for this geographical area and clearly displays the effects ofsome of the terms discussed above. Areas that have few or no roads orthe roads go uphill will be penalized by the present model, and that isprecisely what can be observed on the western part 1166 of thecalculated contour. In cases where the terrain slopes downhill and theroads happen to be aligned along radial directions, as in the case ofcontour sections 1168 and 1170 we observe enhancements and the coverageactually goes beyond the reference circle. In one instance, contoursection 1172 we observe the interplay of terrain and roads. Even thoughthe terrain goes downhill, and an enhancement is expected, there are fewroads and they are not aligned with the radials, causing a zig-zag shapethat decreases the range in that direction. Finally, near contoursection 1174 we observe a deep decrease in range, which is simply aresolution artifact. These sample calculations have been done at verylow resolution, using M=16 angles, which means a resolution of 22.5degrees. In practice, the resolution could be adaptive, by running at alow resolution when a parameter such as the vehicle location changes, toprovide instantaneous results and then refine them by running extraradials.

FIG. 17 generally illustrates a computerized range analysis apparatus1344 capable of performing the required operations. It may consist of aportable or in-dash vehicle navigation device, it may consist of asmart-phone device, or it may consist of any type of computer systemthat interprets and executes software instructions. The apparatus doesnot need to be installed in the vehicle, but rather, it can be placed insome stationary location and it would interact with the vehicle viawireless access. The main component is the range analyzer 1346, whichcoordinates the collection of the necessary input data from theappropriate databases and the processing of the instructions provided bythe user, to calculate the vehicle's range. The user would enter datainto this apparatus with the help of the usual interactive devices 1345,such as a keyboard, a mouse, a touch-sensitive pad or display, etc. Inan alternative configuration these devices can be replaced or augmentedwith a microphone and voice recognition means to enable the user tointeract with the range analyzer. The display device 1347 is used todisplay the results of the range calculations. Alternatively, thedisplay device can be omitted or augmented with another output devicesuch as voice instructions, a printer or hard disk, to which any datanormally displayed to an operator can be sent.

The array of waypoints that describe a route are obtained from a routingmodule 1348, which can be any navigation system that provides detaileddriving directions. For the case of a single route the user can enterthe destination address or its latitude/longitude coordinates, and thestarting point can be either obtained directly from a device thatprovides location services such as the global positioning system (GPS)or it can be entered manually by the user. Alternatively, the rangeanalyzer module 1346 can access a roads database 1350 and provide theroad data to the routing module 1348. The roads database can contain, inaddition to the road coordinates, information such as road type(highway, city street, unpaved road, etc.), driving speed information,etc. The tractive force information can be stored in a database 1349that will contain rolling resistance information for a variety of roadtypes, as well as drag coefficients and frontal area data for vehiclesof interest. Finally, the terrain database 1351 contains digital terrainmaps that can be used by the range analyzer 1346 to associate a groundelevation with each waypoint and to subsequently evaluate the slopeangle of each segment.

FIG. 18 shows a typical configuration for the range analyzer. It wouldrun continuously, updating the predicted range results as the vehiclemoves. The loop starts with an update 1421 of the current location,followed by a refresh 1422 of the current user settings to check if theuser now wishes a different kind of analysis or to modify any of theuser-supplied data, or perhaps quit the application. It proceeds withthe range calculation 1424 followed by the real-time refresh 1425 of thedisplay.

FIG. 19 shows an example of the possible processing that the rangeanalysis 1424 could perform. The first step 1551would gather the vehicledata. Some parameters such as the weight, drag coefficient, and frontalarea need to be obtained only once, but the location would ideally beobtained on a continuous basis. Step 1552 gathers the EPA-like referenceparameters while step 1553 collects the current user settings. At thispoint, we have the necessary information to calculate in step 1554 theaverage ratios Γ and Δ. Based on the user's input, the processingbranches 1555 into contour 1556 or single-route 1557 analysis. Detailsof the contour processing can be found in FIG. 10 while the single-routeprocessing can be found in FIG. 6.

What is claimed is:
 1. A method for determining range of a vehiclecomprising: obtaining information concerning an estimated range for thevehicle; determining a route to a destination along roads available tobe followed by the vehicle; dividing the route into a number of roadsegments; for each such road segment being followed by the vehicle,determining whether the respective road segment is of a certain type ofroad segment; and adding a factor to a running sum based on the type ofroad segment; and adjusting the estimated range based on the runningsum, to determine a location along the route where a remaining energyavailable for the vehicle to follow the route will reach a predeterminedlevel.
 2. The method of claim 1 wherein adjusting the estimated rangefurther comprises continuously adjusting the range according toenvironmental conditions.
 3. The method of claim 2 wherein theenvironment conditions comprise determining whether the vehicle hasactually followed a particular road segment of a particular type alongthe route.
 4. The method of claim 1 wherein adjusting the estimatedrange additionally comprises: continuously averaging the estimated rangeto account for an operating state of a vehicle accessory.
 5. The methodof claim 1 wherein a different estimated range is used depending upon anoperating state of a vehicle accessory.
 6. The method of claim 1 whereinthe information concerning the type of road segment is taken from astored map.
 7. The method of claim 1 wherein the estimated range isderived from a fixed expected ratio of road types that include highwayand city.